The largest sphere is carved out of a cube of side 10.5 cm. Find the r

1.	The largest sphere is carved out of a cube of side 10.5 cm. Find the ratio of their volumes.
Answer» Largest sphere that can be carved out of a cube will have its diameter as the side of the cube. Radius of the largest sphere carved out of a cube of side 10.5 cm = \(\frac{10.5}{2}\) = 5.25 cm Volume of a cube = side³ Volume of a sphere = \(\frac{4}{3}\)πr³ Ratio of their volumes = \(\frac{\frac{4}{3}\pi\times5.25^3}{(10.5)^3}\) = \(\frac{4}{3}\) x \(\frac{22}{7}\) x \(\frac{1}{8}\) = 11 : 21

The largest sphere is carved out of a cube of side 10.5 cm. Find the ratio of their volumes.

Answer»

Largest sphere that can be carved out of a cube will have its diameter as the side of the cube.

Radius of the largest sphere carved out of a cube of side 10.5 cm = \(\frac{10.5}{2}\) = 5.25 cm

Volume of a cube = side³

Volume of a sphere = \(\frac{4}{3}\)πr³

Ratio of their volumes = \(\frac{\frac{4}{3}\pi\times5.25^3}{(10.5)^3}\)

= \(\frac{4}{3}\) x \(\frac{22}{7}\) x \(\frac{1}{8}\)

= 11 : 21